Improved evolutionary optimization from genetically adaptive multimethod search

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   Fig. 1.

   Generated Pareto-optimal fronts after 25, 50, and 75 generations with the NSGA-II (squares), PSO (circles), AMS (+), DE (diamonds), and AMALGAM (x) optimization algorithms for test problem ZDT4. This benchmark problem has 21⁹ different local Pareto-optimal fronts in the search space, of which only one corresponds to the global Pareto-optimal front. Combining the individual algorithms into a simultaneous multimethod search algorithm ensures a faster and more reliable solution to multiobjective optimization problems.

   
   
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   Fig. 2.

   Illustration of the concept of self-adaptive offspring creation. (A) Evolution of the number of offspring points generated with the NSGA-II (squares), PSO (circles), AMS (+), and DE (diamonds) algorithms within AMALGAM's multimethod search as function of generation number for test problem ZDT4. (B) The hypervolume convergence metric for AMALGAM and each algorithm used individually. These results illustrate the utility of individual search algorithms during different stages of the optimization, and provide numerical evidence of Wolpert and Macready's “No Free Lunch” theorem, showing that it is impossible to develop a single search algorithm that will always be superior to any other algorithm (16).

   
   
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   Fig. 3.

   Nondominated solutions found for test problem DTLZ6 (23) with NSGA-II and AMALGAM after 100,000 and 5,000 function evaluations, respectively. (A) The dark line marks the true Pareto-optimal front. Although classical multiobjective methods have difficulty finding solutions on the Pareto front, the AMALGAM method perfectly converges to the true solution set in far fewer function evaluations. (B) Self-adaptive offspring creation by varying the relative importance of the individual algorithms during the optimization is the breakthrough that enables this improvement.